Traveller and many other OSR games treat psionics as a finite resource. You have a certain number of points to spend and they come back slowly. This is by and large a good thing as character running around torching people's minds, reading pin numbers and glomming state secrets and plot points at will is not a good thing.
Only it ignores a central tenet of psionics. You can't just turn them off. My solution is simple. When you pay the points you control the psionics. The referee (me!) has an equal number of these points however and he (me again!) can use them to trigger your psionics when he chooses.
So you maybe buying some gear (all right, call it what it is, -ammunition) when it suits the story for you to have a sudden vision of your patron Baron Sademi performing a human sacrifice ritual. You gotta love post-cognition. Or you're boarding the express train from the capital to the starport and your ship when the great rush of commuters causes the equivalent of a mental assault. Limiting the referee to the same number of points as the player character makes things seem a little more fair to me. The referee should not get to mind blast you every time you ride a lift with three or more people or throw psychic flashes at you willy nilly.
As an alternative the referee might increase or decrease his share of points based on local factors. A high population world might make for more feedback reducing the number of incidents of rogue psionic events or whatever else the referee decides. Jump space might increase the points because FTL always does weird things. Finally the referee might reduce his share of points after the player receives formal training from an institute or teacher above and beyond the initial procedure. If you want a wild psionic who just manifests with no formal training you can work out just how many extra points the referee will get if you want to start with an active psionic (beware agreements signed in blood as always.)
A good rule of thumb would be an unawakened psionic would need to be in the upper 10% power wise before they start experiencing poltergeist events and waking nightmares.
Now taking psionic medications becomes a little more interesting too. As the psi drugs increase your psionic points they increase the points available to the referee (me yet again!!).
This system can cause some problems if the psionic is capable of teleporting. The referee is encouraged to be a good sport. Porting a character out of his battledress, for example, may lead to ugly (real life) scenes. It also probably isn't funny after the first time. Porting a pc out of the shower into a public area likewise is probably done sparingly. However a kindly referee might allow a 'porter to make a jump when he is out of energy in a life or death situation. Again you might not take your armor with you, or your undergarments.
So you can have your resource allocation. The referee can have his fun too, set up foreshadowing, and remind the players psionics is not just something they can turn on and off like in the comic books. he can even throw them a freebie sometimes ("That Baron Sademi is bad news!") or give them a red herring ("Baron Sademi ... was in community theater you idiot!" "... Before or after he sacrificed that person?")